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We consider the online scheduling problem of minimizing total weighted flowtime plus energy in the dynamic speed scaling model, where a processor can scale its speeddynamically between 0 and some maximum speed T. In the past few years this problem hasbeen studied extensively under the clairvoyant setting, which requires the size of a job tobe known at release time [1, 4, 5, 8, 15, 18–20]. For the non-clairvoyant setting, despite itspractical importance, the progress is relatively limited. Only recently an online algorithmLAPS is known to be O(1)-competitive for minimizing (unweighted) flow time plus energyin the infinite speed model (i.e., T = ¥) [11, 12]. This paper makes two contributions tothe non-clairvoyant scheduling. First, we resolve the open problem that the unweightedresult of LAPS can be extended to the more realistic model with bounded maximum speed.Second, we show that another non-clairvoyant algorithm WRR is O(1)-competitive whenweighted flow time is concerned. Note that WRR is not as efficient as LAPS for schedulingunweighted jobs as WRR has a much bigger constant hidden in its competitive ratio.published_or_final_versio

Non-clairvoyant scheduling for weighted flow time and energy on speed bounded processors